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Oliga [24]
3 years ago
8

18. How many milliliters of water at 23 °C with a density of 1.00 g/mL must be mixed with 180 mL (about 6 oz) of coffee at 95 °C

so that the resulting combination will have a temperature of 60 °C? Assume that coffee and water have the same density and the same specific heat.
Chemistry
1 answer:
sveticcg [70]3 years ago
3 0

Answer:

The number of water that must be mixed in the solution is 170.27 mL

Explanation:

given information :

Temperature of water (T_{1}) = 23^{o}C

density of water (ρ) = 1.00 g/mL

Temperature of coffee  (T_{1}) = 95^{o}C

volume of coffee (V_{2}) = 180 mL

Mixed Temperature (T_{mix}) = 60^{o}C

to calculate the heat, w use the formula :

Q = m x c x ΔT

where

m = mass of the substance (g)

c = specific heat (J/g^{o}C)

ΔT = the temperature change (^{o}C)

in the mixture solution, the heat of the water (Q_{1}) should be the same as the heat of coffee (Q_{2}). Thus,

Q_{1} = Q_{2}

m_{1} x c_{1} x ΔT_{1} = m_{2} x c_{2} x ΔT_{2}

where

m_{1} is the mass of water

m_{2} is the mass of coffee

c_{1} is the specific heat of water

c_{2} is the specific heat of coffee

Assume coffee and water have the same specific heat. So,

c_{1} = c_{2}, we can remove it from the equation.

Hence.

m_{1} x ΔT_{1} = m_{2} x ΔT_{2}

we know that

ρ = \frac{m}{V}

m = ρ x V, subtitute it to the equation:

ρ_{1} x V_{1} x ΔT_{1} = ρ_{2} x V_{2} x ΔT_{2}

V_{1} is the volume of water

coffee and water have the same density, so we can remove the formula

V_{1} x ΔT_{1} = V_{2} x ΔT_{2}

V_{1} = (V_{2} x ΔT_{2}) / ΔT_{1}

V_{1} = V_{2} x (\frac{(T_{2} - T_{mix}) }{(T_{mix} - T_{1})}

V_{1} = 180 mL x \frac{(95-60)^{o}C}{(60-23)^{o}C}

V_{1} = 180 mL x \frac{(35)^{o}C}{(37)^{o}C}

V_{1} = 170.27 mL

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